Pseudodecahedron
- To: mathgroup at smc.vnet.net
- Subject: [mg54010] Pseudodecahedron
- From: Roger Bagula <tftn at earthlink.net>
- Date: Mon, 7 Feb 2005 03:12:58 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I found this surface last night. It has the same angles and face number as a Dodecahedron and is made by a parametric algorithm. If you take the second Pi/5 rotation out, it is a 12 sided surface with ten quadralateral ( four sided) faces and two pentagon faces. It uses a five sided and a 6 ( double 3) sided function set. I call the result a psedodecahedron. --------------------------------------------------------------- Mathematica notebook (* 5 sided measure function*) a5 = Max[Table[Cos[t + 2*Pi*n/5], {n, 0, 4}]] (* six sided measure function*) a3 = Max[Table[Abs[Cos[p + 2*Pi*n/3]], {n, 0, 2}]] x = (Sin[p]/a3)*Sin[t]/a5; y = (Sin[p]/a3)*Cos[t]/a5; z = Cos[p]/a3; (* rotated bottom section by Pi/5*) x1 = x*Cos[Pi/5] - Sin[Pi/5]*y; y1 = y*Cos[Pi/5] + Sin[Pi/5]*x; z1 = z; g = ParametricPlot3D[{x, y, z}, {t, -Pi, Pi}, {p, 0, Pi/2}, PlotPoints->60, Axes -> False, Boxed -> False]; g1 = ParametricPlot3D[{x1, y1, z}, {t, -Pi, Pi}, {p, Pi/2, Pi}, PlotPoints -> 60, Axes -> False, Boxed -> False]; Show[{g, g1}] Show[{g, g1}, ViewPoint -> {-0.001, -0.416, -3.358}] Show[{g, g1}, ViewPoint -> {-0.080, -3.375, -0.229}] ---------------------------------------------------------------- Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn